Question: Find the slope and y-intercept of the line that is ${\text{parallel}}$ to $\enspace {y = 3x - 4}\enspace$ and passes through the point ${(-3, -3)}$. {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {1} {2} {3} {4} {5} {6} {7} {8} {9} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9}
Answer: Parallel lines have the same slope. The slope of the blue line is ${3}$ , so the equation of our parallel line will be of the form $\enspace {y = 3x + b}\enspace$ We can plug our point, $(-3, -3)$ , into this equation to solve for ${b}$ , the y-intercept. $-3 = {3}(-3) + {b}$ $-3 = -9 + {b}$ $-3 + 9 = {b} = 6$ The equation of the parallel line is $\enspace {y = 3x + 6}\enspace$. ${m = 3, \enspace b = 6}$